4. Probability
Basic Concepts of Probability
1:40 minutesProblem 4.r.13b
Textbook Question
National Statistics Day
b. If a person is randomly selected, find the probability that his or her birthday is in October. Ignore leap years.
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the probability that a randomly selected person's birthday falls in the month of October. Assume there are no leap years, so the year has 365 days.
Step 2: Determine the total number of days in a year. Since we are ignoring leap years, the total number of days in a year is 365.
Step 3: Determine the number of days in October. October has 31 days.
Step 4: Use the formula for probability. The probability of an event is given by the formula: \( P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Here, the favorable outcomes are the 31 days in October, and the total outcomes are the 365 days in a year.
Step 5: Substitute the values into the formula. Replace the numerator with 31 (days in October) and the denominator with 365 (total days in a year). Simplify the fraction if needed to express the probability in its simplest form.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it quantifies the chance of randomly selecting a person whose birthday falls in October. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.
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Sample Space
The sample space is the set of all possible outcomes in a probability experiment. For the birthday problem, the sample space consists of the 12 months of the year. Understanding the sample space is crucial for calculating probabilities, as it provides the total number of outcomes against which favorable outcomes are compared.
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Favorable Outcomes
Favorable outcomes refer to the specific outcomes in the sample space that satisfy the condition of interest. In this case, the favorable outcomes are the days in October, which total 31. Identifying favorable outcomes is essential for calculating the probability of an event, as they directly influence the numerator in the probability formula.
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